Geodesic
The purity of a completion
Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 127-129

Voir la notice de l'article provenant de la source Cambridge University Press

This note establishes two statements from R. M. Fossum's review [1] of a paper by E. A. Magarian [2]. Firstly, if A → B is a pure homomorphism (of commutative rings) then A[[x1,...,xs]] → B[[x1,..., xs]] is pure. Secondly, if Rn → R is a directed family of pure homomorphisms then ∪ Rn → R is pure. A consequence is that if Rn → R is a directed family of pure homomorphisms and if R is Noetherian, then ∪ Rn[[x1,...,xs]]is Noetherian. 
Jr, S. H. Cox. The purity of a completion. Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 127-129. doi: 10.1017/S0017089500002846
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[2] 2.Magarian, E. A., Direct limits of power series rings, Math. Scand. 31 (1972), 103–110. Google Scholar | DOI

[3] 3.Gilmer, R. and Mott, J., Some results on contracted ideals, Duke Math. J. 37 (1970), 751–767. Google Scholar | DOI

[4] 4.Enoch, E. E., On absolutely pure modules, Preprint, University of Kentucky. Google Scholar

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[7] 7.Gilmer, R., Contracted ideals in Krull domains, Duke Math. J. 37 (1970), 769–774. Google Scholar | DOI

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